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Many introductory texts will tell you that in Haskell type signatures are "almost always" optional. Can anybody quantify the "almost" part?
As far as I can tell, the only time you need an explicit signature is to disambiguate type classes. (The canonical example being read . show.) Are there other cases I haven't thought of, or is this it?
(I'm aware that if you go beyond Haskell 2010 there are plenty for exceptions. For example, GHC will never infer rank-N types. But rank-N types are a language extension, not part of the official standard [yet].)
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From HaskellWiki. A type signature is a line like. inc :: Num a => a -> a. that tells, what is the type of a variable. In the example inc is the variable, Num a => is the context and a -> a is its type, namely a function type with the kind * -> * .
In Haskell, every statement is considered as a mathematical expression and the category of this expression is called as a Type. You can say that "Type" is the data type of the expression used at compile time.
If you need to figure out what the type of an object is in a Haskell program, I hope this is helpful. Note that if you are in GHCI, you can just put :type before your expression to determine the expression's type, or use :set +t to see the type of every expression in GHCI.
Polymorphic recursion needs type annotations, in general.
f :: (a -> a) -> (a -> b) -> Int -> a -> b f f1 g n x = if n == (0 :: Int) then g x else f f1 (\z h -> g (h z)) (n-1) x f1 (Credit: Patrick Cousot)
Note how the recursive call looks badly typed (!): it calls itself with five arguments, despite f having only four! Then remember that b can be instantiated with c -> d, which causes an extra argument to appear.
The above contrived example computes
f f1 g n x = g (f1 (f1 (f1 ... (f1 x)))) where f1 is applied n times. Of course, there is a much simpler way to write an equivalent program.
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